Question

what is the resistance of the wire if its length is 200 m long and its diameter is 0.4 mm and its resistivity is 3.2 times 10 the power of -8

Answer 1

Given:

$\tt{\longmapsto Length = 200m}$

$\tt{\longmapsto Diameter = 0.4mm}$

$\tt{\longmapsto Resistivity = 3 \times 10^{-8}}$

To find:

We need to find the resistance of the wire.

Formula used:

$\tt{\longmapsto Resistance = \dfrac{\rho \times l}{a}}$

Here,

• $\tt{Resistivity = \rho}$
• $\tt{l = Length}$
• $\tt{a = Area\:of\:cross-section}$

Solution:

Before moving onto the problem, we should first find the radius of wire.

We know that diameter of the wire is 0.4 mm. By converting it to metre, we get 0.4 × $0.4^{-3}$ m.

$\tt{\longmapsto Radius = \dfrac{Diameter}{2}}$

$\tt{\longmapsto Radius = \dfrac{0.4 \times 10^{-3}}{2}}$

$\tt{\longmapsto Radius = 0.2 \times 10^{-3} m}$

Let us apply our formula to find the resistance of the wire.

$\tt{\longmapsto Resistance = \dfrac{\rho \times l}{a}}$

$\tt{\longmapsto Resistance = \dfrac{\rho \times l}{\pi r^2}}$

$\tt{\longmapsto Resistance = \dfrac{3 \times 10^{-8} \times 200}{\pi (0.2 \times 10^{-3})^2}}$

We know that pi = 22/7. Since, its on the denominator side, it becomes 7/22 when taken as reciprocal.

$\tt{\longmapsto Resistance = \dfrac{3 \times 10^{-8} \times 200 \times 7}{22 \times 0.04 \times 10^{-6}}}$

$\tt{\longmapsto Resistance = \dfrac{3 \times 10^{-2} \times 100 \times 7}{11 \times 0.04}}$

$\tt{\longmapsto Resistance = \dfrac{3  \times 7}{11 \times 0.04}}$

$\tt{\longmapsto Resistance = \dfrac{21}{0.44}}$

$\tt{\longmapsto Resistance = 47.72\:or\:48\:ohm}$

Hence, the resistance of the wire is 48 ohm.

(Note: The resistance is approximately equal to 48 ohm and its not the accurate answer.)